Note to Frequency Calculator

Sound frequency and pitch are directly related: frequency, measured in hertz (cycles per second), determines what pitch we hear. The Western musical scale is built on a logarithmic system where each octave doubles the frequency, and each of the 12 semitones within an octave divides that doubling equally.

Frequency of any note formula: f = f₀ × 2^(n/12)

Where:

• f = frequency of the target note (Hz)
• f₀ = reference frequency (standard tuning: A4 = 440 Hz)
• n = number of semitones above (positive) or below (negative) the reference note
• 2^(1/12) = the twelfth root of 2, about 1.05946, which is the frequency ratio between adjacent semitones

Frequency ratios of musical intervals:

• Unison: 1:1
• Minor 2nd (1 semitone): 1.0595:1
• Major 2nd: 1.1225:1
• Minor 3rd: 1.1892:1
• Major 3rd: 1.2599:1
• Perfect 4th: 1.3348:1
• Perfect 5th: 1.4983:1
• Octave: 2:1 exactly

Standard note frequencies (A440 tuning):

• A3: 220 Hz; A4: 440 Hz; A5: 880 Hz
• Middle C (C4): 261.63 Hz
• B4: 493.88 Hz; C5: 523.25 Hz

Wavelength formula: λ = v ÷ f Where v = speed of sound ≈ 343 m/s at 20°C, f = frequency in Hz.

Worked example:

Start with C5. Middle C is C4 at 261.63 Hz, and C5 sits one octave above it, so the exponent is a full 12 semitones:

• C5 = 261.63 × 2^(12/12) = 261.63 × 2 = 523.25 Hz

Now D4, counted from the A440 reference. The trap here is direction. D4 is below A4, not above it, so n comes out negative. Count down the chromatic scale and it is seven steps:

A4 → G♯4 → G4 → F♯4 → F4 → E4 → D♯4 → D4, so n = -7

• f(D4) = 440 × 2^(-7/12) = 440 × 0.66742 = 293.66 Hz

Getting the sign backwards is the single most common mistake with this formula. Had you used +7 you would have landed on E5 at 659.26 Hz, more than an octave adrift.

Wavelength, and why it matters for a room

The wavelength line in the result panel is not decoration. A 40 Hz bass note is an 8.6 meter wave, which is longer than most living rooms, so the room cannot support it evenly and you get the boom and null pattern every home studio fights. Middle C at 261.63 Hz is 1.31 m, comfortably inside a room, and C8 at 4,186 Hz is only 8.2 cm, short enough that a cushion absorbs it.
That is the whole reason bass traps are enormous and treble panels are thin.